| 粟涓,董新汉.双正交小波滤波器簇代数结构及构造[J].数学年刊A辑,2014,35(4):451~462 |
| 双正交小波滤波器簇代数结构及构造 |
| Algebraic Structure and Construction of Bi-orthogonal Filter Banks |
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| DOI： |
| 中文关键词: 双正交小波,滤波器,多相向量,多相矩阵,消失矩 |
| 英文关键词:Bi-orthogonal wavelets, Filter bank, Polyphase vector, Polyphase matrix, Vanishing moment |
| 基金项目:国家自然科学基金 (No.11171100) 和
高等学校博士学科点专项科研基金(No.20134306110003) |
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| 中文摘要: |
| 研究了一类向量多项式两种特殊分解结构,由此引进了与双正交小波滤波器簇相应的多相向量概念, 分析了多相向量分解代数结构, 得到了在低通滤波器给定条件下,
满足任意阶可和规则的对偶低通滤波器构造方法.分析并证明了双正交滤波器簇对应多相向量至多具有
的3种代数分解结构, 根据其分解的形式得到了双正交小波基构造的新方法,该方法便于双正交小波构造计算机程序化. |
| 英文摘要: |
| This paper deals with the special algebraic
structure of a class of vector polynomial,
thus polyphase vector and polyphase matrix of multi-band bi-orthogonal wavelet filter banks are defined.
The authors analyse especial decomposition algebraic structure of
polyphase vector, and obtain a method for constructing dual
scaling filter banks with any order of polynomial preservation
when scaling filter bank is given. It is proved that any bi-orthogonal
wavelet polyphase vector of scaling filter banks pair can be
factored as the product of three kinds of algebraic structures at
most. A new method is presented to design all high-pass filter
banks corresponding to the given scaling low-pass filter banks.
The method is convenient for construction of bi-orthogonal
wavelets with computer program. |
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